1. Field of the Invention
The present invention generally relates to an optical scanning device, a scanning optical system, an optical scanning method and an image forming apparatus.
2. Description of the Related Art
Optical scanning devices have been widely used in image forming apparatuses such as a digital copier, an optical printer, a facsimile apparatus and so forth. Recently, a request for image quality in images formed by the image forming apparatuses have become severe. Thereby, improvement in performance of the optical scanning devices has been demanded.
xe2x80x98A writing densityxe2x80x99 is one factor which directly affects image quality of images formed through optical writing by the optical scanning device. As the writing density is increased, the resolution of images formed increases, and, thereby, it is possible to form clear and smooth images.
In order to increase the writing density (dpi), it is necessary to reduce the diameter of a beam spot formed on a surface to be scanned by the optical scanning device.
Ideally, the spot diameter is a beam spot diameter of a deflected light beam. However, when a curvature of field occurs, it is not possible that the image surface of the deflected light beam coincides with the surface to be scanned completely, and, thereby, the spot diameter varies as the image height varies. Accordingly, in order to render xe2x80x98a stable beam spotxe2x80x99 having a small variation in spot diameter, it is necessary to well correct the curvature of field of the optical scanning system. In the related art, there are many scanning optical systems in which the curvature of field is well corrected.
When an optical system of the optical scanning device is assembled, an error in precision of assembly inevitably occurs. Accordingly, even when the curvature of field is well corrected in a design stage, it may not be possible that the image surface of the scanning optical system coincides with the surface to be scanned according to the design. When the image surface is separate from the surface to be scanned due to an influence of assembling error or the like, the spot diameter of the beam spot formed on the surface to be scanned becomes larger than the spot diameter according to the design.
Accordingly, when the scanning optical system of the optical scanning device is designed, xe2x80x98a certain degree of separationxe2x80x99 of the image surface from the surface to be scanned due to assembling error or working error is assumed, and, a design is made such that, even when the image surface is separate from the surface to be scanned, the variation in the spot diameter of the beam spot on the surface to be scanned should fall within xe2x80x98an allowable rangexe2x80x99.
A position of a beam waist of the scanning beam is located on the image surface. Accordingly, a difference between the position of the beam waist and the surface to be scanned is called xe2x80x98defocusxe2x80x99.
A range in defocus such that the variation in spot diameter due to the defocus falls within the allowable range is called xe2x80x98allowable depthxe2x80x99, and, a characteristic curve indicating a relationship between th defocus and spot diameter is called xe2x80x98depth curvexe2x80x99.
A practical xe2x80x98satisfactory scanning optical systemxe2x80x99 is an optical system having a satisfactory optical performance of design, and, also, having a proper allowable depth such that xe2x80x98an excessive precisionxe2x80x99 is not requested to assembling and working.
Japanese Laid-Open Patent Application (Kokai) No. Hei 10-232358 discloses an optical system rendering a beam spot having a small diameter. This optical system is such that a scanning optical system condensing a deflected beam toward a surface to be scanned includes three or four lenses, and the beam spot having a very small diameter of 30 xcexcm for a wavelength of 780 nm used is rendered, and an allowable depth of 1 mm is rendered.
It is considered that it is very difficult to reduce the diameter of a beam spot while the allowable depth is secured to be more than approximately 1 mm for a wavelength more than 700 nm used.
Employing a beam having a short wavelength is effective for reducing the diameter of a beam spot as is well known. In principle, it is possible to reduce the diameter of a beam spot in proportion to a wavelength used. For a semiconductor laser which is generally used as a light source of the optical scanning device, a wavelength of light emitted therefrom is reduced, and, xe2x80x98a short wavelength equal to or shorter than 400 nmxe2x80x99 is being rendered. For an excimer laser, a wavelength of 200 nm has been already rendered.
In principle, it is possible to reduce a diameter of a beam spot by employing a light source of a short wavelength. However, when simply reducing a diameter of a beam spot, the allowable depth becomes narrower accordingly.
In the related art, it is not known to secure xe2x80x98a necessary allowable depthxe2x80x99 while reducing a diameter of a beam spot employing a light source of a wavelength shorter than 600 nm, that is, xe2x80x98an art such as to render both reduction of diameter of beam spot employing a short wavelength and satisfactory allowable depthxe2x80x99.
An object of the present invention is to reduce a diameter of a beam spot employing a light source for optical scanning of a short wavelength, and, also, to secure a necessary allowable depth.
An optical scanning device according to the present invention, comprises:
an aperture shaping a beam from a light source;
a light deflector deflecting the beam; and
a scanning imaging optical system condensing the deflected beam toward a surface to be scanned so as to form a beam spot on the surface to be scanned,
wherein:
a wavelength xcex of the beam emitted by the light source satisfies:
350 (nm)xe2x89xa6xcexxe2x89xa6600 (nm)xe2x80x83xe2x80x83(1)
and,
a desired diameter xcfx86 of the beam spot and the wavelength xcex satisfy:
0.5 (mm)xe2x89xa6xcfx862/xcexxe2x89xa66 (mm)xe2x80x83xe2x80x83(2)
The above-mentioned spot diameter xcfx86 means a diameter of an area through which the light intensity is equal to or higher than 1/e2 where the intensity distribution of the beams spot is normalized so that the maximum value in the intensity distribution becomes 1. Based on the above-mentioned conditional formula (2), the range of the spot diameter xcfx86 is 17.3 through 60 xcexcm when the wavelength xcex=600 (nm); and the range of the spot diameter xcfx86 is 13.2 through 46 xcexcm when the wavelength xcex=350 (nm). It is possible to render the beam spot having the spot diameter in this range with a practical allowable depth.
Further, the following conditions (the range of the xcex is further limited, and the desired spot diameter xcfx86 and wavelength xcex are further limited) may be satisfied:
350 (nm)xe2x89xa6xcexxe2x89xa6500 (nm)xe2x80x83xe2x80x83(3)
xe2x80x830.5 (mm)xe2x89xa6xcfx862/xcexxe2x89xa63 (mm)xe2x80x83xe2x80x83(4)
and,
a root-mean-square value RMS(wavefront aberration) of wavefront aberrations on a surface of an exit pupil may satisfy:
RMS(wavefront aberration)xe2x89xa60.2xe2x80x83xe2x80x83(5)
Thereby, it is possible to render the satisfactory beam spot having a smaller diameter.
There, the above-mentioned xe2x80x98exit pupilxe2x80x99 means an image of the aperture (image of the opening thereof) formed through the optical system disposed on the surface-to-be-scanned side of the aperture.
The above-mentioned root-mean-square value RMS(wavefront aberration) of the wavefront aberrations on the surface of the exit pupil is calculated as follows:
The wave surface of the beam on the surface of the exit pupil is divided into N area elements having the minute areas same as each other. Then, the root-mean-square value is calculated from the maximum wavefront aberrations Wi (i=1, 2, 3, . . . , N) for the respective i-th area elements according to the well-known definition of root mean squire. The method of dividing the wave surface into area elements may be a method such that squares are obtained, a method such that concentric circular areas or concentric elliptical areas are obtained, or the like. The number N of the thus-obtained area elements is preferably equal to or larger than 100. When the number N is as large as such an order, the RMS(wavefront aberration) does not depend on the method of dividing into the area elements substantially.
It is preferable that an angle xcex8 formed on a main scan plane (plane which the chief ray of the deflected beam deflected ideally traces) between a normal of the surface to be scanned and any scanning beam satisfies:
cos xcex8xe2x89xa70.9xe2x80x83xe2x80x83(6)
The shape of the opening of the aperture is basically rectangular. However, an elliptical shape obtained as a result of the four corner of a rectangle are rounded smoothly, a hexagon, an octagon, a circle, an ellipse, or the like is also allowable.
Further, the light source may comprise a semiconductor laser. In this case, the divergent beam emitted from the light source may be coupled by a coupling optical system to the subsequent optical system, and the thus-coupled beam may be shaped by the aperture. As the above-mentioned coupling optical system, a coupling mirror can be used. However, a coupling lens or a diffraction grating may also be used.
The function of the coupling optical system may be a function of transforming a divergent light beam from the semiconductor laser into a divergent beam in which the divergence is weakened, a function of transforming into a parallel beam, or a function of transforming into a convergent beam.
The coupling optical system may comprise a coupling lens, and the coupling function thereof may comprise a collimating function.
The light deflector may comprise a rotary mirror (rotary mono-surface mirror, a rotary bi-surface mirror, or a rotary polygon mirror) comprising a deflection reflective surface(s); and
the device may further comprise a line-image imaging optical system imaging a line image long in a main scan direction on or in the vicinity of the deflection reflective surface, from the coupled beam.
As the light source, an excimer laser mentioned above, various types of gas laser, solid laser, LED or the like may be also used, other than the above-mentioned semiconductor laser.
As the above-mentioned line-image imaging optical system, a convex cylindrical lens, or a concave cylindrical mirror may be used.
As the light deflector, a swinging mirror such as a galvano mirror may also be used, other than the rotary mirror.
The scanning imaging optical system condensing the beam deflected by the light deflector toward the surface to be scanned may consist of at least single lens, at least single imaging mirror having an imaging function, or a mixture of at least one lens and at least one imaging mirror.
A scanning optical system according to the present invention is used in an optical scanning device comprising an aperture shaping a beam from a light source, a light deflector deflecting the beam, and a scanning imaging optical system condensing the deflected beam toward a surface to be scanned so as to form a beam spot on the surface to be scanned. The scanning optical system directs the beam from the light source which emits light having a predetermined wavelength xcex which falls within a range such that:
350 (nm)xe2x89xa6xcexxe2x89xa6600 (nm)xe2x80x83xe2x80x83(1)
to the surface to be scanned so as to form the beam spot thereon;
the scanning optical system comprises at least the aperture, light deflector and scanning imaging optical system; and
the scanning optical system satisfies the following conditional formulas for a desired diameter of the beam spot xcfx86:
0.5 (mm)xe2x89xa6xcfx862/xcexxe2x89xa66 (mm)xe2x80x83xe2x80x83(2)
xcfx86=0.7xcex/(f/a)xe2x80x83xe2x80x83(7)
where f denotes a distance from an exit pupil of the optical system (image of the aperture formed by this optical system) disposed on the the-surface-to-be-scanned side of the aperture to an image surface of the scanning imaging optical system (in an ideal case, coincides with the surface to be scanned), and 2a denotes a diameter of the aperture on a surface of the exit pupil.
In the above-mentioned scanning optical system, the following condition formulas (for the range of the predetermined wavelength xcex and condition for the desired spot diameter xcfx86 and predetermined wavelength xcex) may be satisfied:
350 (nm)xe2x89xa6xcexxe2x89xa6500 (nm)xe2x80x83xe2x80x83(3)
0.5 (mm)xe2x89xa6xcfx862/xcexxe2x89xa63 (mm)xe2x80x83xe2x80x83(4)
and,
a root-mean-square value RMS(wavefront aberration) of wavefront aberrations on the surface of the exit pupil may satisfy:
RMS(wavefront aberration)xe2x89xa60.2xe2x80x83xe2x80x83(5)
Further, the field angle of the scanning imaging optical system may be set preferably such that an angle xcex8 formed on a main scan plane (plane which the chief ray of the deflected beam ideally deflected traces) between a normal of the surface to be scanned and any scanning beam satisfies:
cos xcex8xe2x89xa70.9xe2x80x83xe2x80x83(6)
Further, the light source may comprise a semiconductor laser. In this case, the divergent beam emitted from the light source may be coupled by a coupling optical system to the subsequent optical system; and the aperture may be disposed on the surface-to-be-scanned side of the coupling optical system. In this case, the coupling optical system may comprise a coupling lens, and the coupling function thereof may comprise a collimating function.
Further, the light deflector may comprise a rotary mirror comprising a deflection reflective surface; and
the system may further comprise a line-image imaging optical system imaging a line image long in a main scan direction on or in the vicinity of the deflection reflective surface, from the coupled beam.
The line-image imaging optical system may comprise a concave cylindrical mirror or a convex cylindrical lens.
The scanning imaging optical system may comprise lenses only. In this case, the scanning imaging optical system may comprise two lenses.
The coupling optical system may comprise a coupling lens, and the coupling function thereof may comprise a collimating function; and
at least one surface of the two lenses of the scanning imaging optical system may comprise a special toroidal surface in which a shape in a main scan section is a non-arc shape, and a shape in a sub-scan section is a non-arc shape and varies in a main scan direction.
An optical scanning method according to the present invention is a method of shaping a beam from a light source by an aperture, deflecting the beam by a light deflector, condensing the deflected beam toward a surface to be scanned by a scanning imaging optical system and forming a beam spot on the surface to be scanned, and, thus, performing optical scanning of the surface to be scanned. The above-mentioned optical scanning device according to the present invention is used in this method.
An image forming apparatus according to the present invention performs optical scanning of a photosensitive surface of a photosensitive medium by an optical scanning device, and forms a latent image thereon, visualizes the latent image so as to obtain a visible image therefrom. The above-mentioned optical scanning device according to the present invention is used in this image forming apparatus for performing the optical scanning of the photosensitive surface of the photosensitive medium.
In the image forming apparatus, the photosensitive medium may comprise a photoconductive photosensitive body, and, the electrostatic latent image formed through uniform charging of the photosensitive surface and optical scanning by the optical scanning device may be visualized into a toner image. The toner image is fixed onto a sheet recording medium (transfer paper, or an OHP sheet (plastic sheet for an overhead projector)).
Alternatively, a film for photography with silver halide may be used as the photosensitive medium, for example. In this case, the latent image formed through the optical scanning by the optical scanning device is visualized by a method of developing in an ordinary process of photography with silver halide. Such an image forming apparatus may be embodied as an optical plate-making system, or an optical drawing apparatus, for example.
The above-mentioned image forming apparatus according to the present invention may be applied to a laser printer, a laser plotter, a digital copier, a facsimile apparatus or the like.
According to the well-known Rayleigh""s formulas, resolution R and focal depth D when a light source emitting a beam of a wavelength xcex is used can be expressed as follows (Journal, O plus E, No. 182, Page 93):
R=k1xc2x7xcex/(NA)xe2x80x83xe2x80x83(1A)
D=k2xc2x7xcex/(NA)2xe2x80x83xe2x80x83(2A)
There, k1 and k2 are proportional coefficients determined by a use of an imaging system and/or circumferential conditions.
The intensity distribution I(X) of a diffracted image formed by a rectangular aperture having a width of 2a, after being normalized so that the maximum intensity becomes 1, can be expressed as follows:
I(X)={sin(aX)/(aX)}2xe2x80x83xe2x80x83(3A)
As X approaches 0, I(X) approaches 1.
FIG. 2 shows the above-mentioned formula (3A). The horizontal axis indicates aX/xcfx80, and the vertical axis indicates the right side of the formula (3A). Assuming that the distance from the surface of the exit pupil to the image surface of the imaging system as xe2x80x98fxe2x80x99, X=2xcfx80x/(xcexxc2x7f). As X has a dimension of reciprocal of length, xe2x80x98xxe2x80x99 has a dimension of length.
As shown in FIG. 2, the formula (3A) is such that I=0 (first local minimum) when aX=xcfx80.
Accordingly,
aX=axc2x72xcfx80x/(xcexxc2x7f)=xcfx80
x=xcexxc2x7f/(2a)=(xcex/2)xc2x7(f/a)
Then, because (f/a) is equal to the numerical aperture NA,
x=(xcex/2)xc2x7NA=(xc2xd)xc2x7xcex/(NA)
The value of xe2x80x98xxe2x80x99 in the above expression is the distance from the center of the intensity distribution shown in FIG. 2 to the first local minimum. Accordingly, the beam diameter xcfx860 which is the distance between the first local minimums is as follows:
xcfx860=2x=xcex/(NA)
This value is one in a case where k1=1 in the above formula (1A).
In a scanning optical system, a spot diameter is expressed by 1/e2 of the central intensity according to the general custom. Accordingly, the right side of xe2x80x98I(X)=1/e2xe2x80x99 is substituted for the left side of the formula (3A), and the thus-obtained formula is solved for aX. Then, aXxcx9c0.7xcfx80. Therefore, the spot diameter xcfx86 expressed by 1/e2 is
xcfx86=0.7xc2x7xcex/(NA)xe2x80x83xe2x80x83(4A)
Accordingly, the wavelength xcex of light emitted by the light source, the spot diameter xcfx86 of the beam spot formed by the scanning optical system and the numerical aperture NA of the optical system disposed on the surface-to-be-scanned side of the aperture satisfy the formula (4A).
In the above-mentioned formula (2A), k2, and, then, the focal depth D, accordingly, varies, in accordance with the allowable range of variation in spot diameter set for the target spot diameter (designed median of spot diameter). When the wavefront aberration is satisfactorily corrected into approximately 0, and variation in spot diameter is controlled to be small, the range of k2 is 0.7 through 1.0.
That is, the allowable range of variation in spot diameter for the target spot diameter xcfx86 is, generally, within xc2x15% through within xc2x120%. When the allowable range is determined as xcfx86(1xc2x10.05), k2=0.7. When the allowable range is determined as xcfx86 (1xc2x10.2), k2=1.0.
The above-mentioned focal depth D gives the value of the range of defocus when the range of variation in spot diameter falls within the range of xcfx86(1xc2x10.05) through xcfx86(1xc2x10.2). Accordingly, it corresponds to the above-mentioned allowable depth. Therefore, the focal depth D is referred to as allowable depth D, hereinafter.
When the allowable depth D is such that D  less than 0.7 (mm), a very high precision and/or adjustment is required in assembling of components, and, a positional precision for peripheral components such as the photosensitive medium acting as the surface to be scanned and so forth becomes severe. Further, it is necessary to control variation in position of the image surface due to environmental variation to be small. For this purpose, it is necessary to use a glass material having a small change in property due to temperature/humidity for the scanning optical system. When a plastic material is used therefor, some measures to cancel the variation should be provided. Accordingly, while a beam spot having a small diameter and having small variation can be rendered, the manufacturing costs increase.
When the allowable depth D is such that 0.7xe2x89xa6Dxe2x89xa610 (mm), the component precision, positional precision, disposition precision of peripheral components can be eased, and, also, some remaining error of property variation due to environmental variation can be allowed. Accordingly, costs can be reduced, and very practical system can be achieved.
When the allowable depth D exceeds 10 mm, and becomes further larger, while the allowable range in component precision, positional precision and so forth becomes large, it is not possible to reduce the diameter of beam spot to a necessary value.
Therefore, according to the present invention, the allowable depth D is determined such that 0.7xe2x89xa6Dxe2x89xa610 (mm), the light source of a short wavelength (350 nm through 600 nm) is used, and, thereby, forming of a small-sized, stable beam spot is achieved.
The above-mentioned conditional formula (2) indicates the condition for this porpoise. When the lower limit 0.5 mm thereof is exceeded, the costs required for the optical materials, component working, positional precision and so forth are very high, and, provision of a practical optical scanning device or scanning optical system becomes difficult. That is, when the lower limit is exceeded, the spot diameter of the beam spot formed is reduced to be smaller than 13 xcexcm (for the wavelength of 350 nm). However, even if the allowable range of variation in spot diameter is set as xcfx86(1xc2x10.2), the allowable depth is equal to or smaller than 0.5 mm, and, thus, is further lower than 0.7 mm. Accordingly, it is not possible to render the optical scanning device and scanning optical system without increase in costs.
Further, when the upper limit of the conditional formula (2) is exceeded, although the allowable depth becomes larger, the spot diameter of the thus-obtained beam spot is, even if xcex=350 nm, larger than 46 xcexcm, and, thereby, there is little significance that the beam spot is made to have a small diameter employing the light source of short wavelength.
When the lower limit 350 nm of the range of wavelength xcex of light emitted by the light source: 350 through 600 (nm) (conditional formula (1)) is exceeded, the transmittance of the plastic lenses is degraded when the plastic lenses are used in the scanning imaging optical system. Even when lenses of optical glass are used therefor, it is necessary to use material having satisfactory transmittance for a short wavelength. Thereby, the costs increase. Further, the material of the optical system disposed on the light-source side of the light deflector is also limited. When the upper limit 600 nm of xcex is exceeded, satisfactory advantage in reduction of diameter of beam spot cannot be obtained.
As a result of the conditional formulas (1) and (2) being satisfied, a satisfactory small spot diameter (for example, 30 xcexcm) can be easily and positively obtained, and a satisfactory allowable depth (equal to or larger than 0.7 mm) can be secured.
In order to achieve a further smaller spot diameter in beam spot, it is necessary to consider influence of wavefront aberration together with the range of wavelength of light emitted by the light source, and the range of the parameter xcfx862/xcex.
For example, in order to obtain the spot diameter of 15 xcexcm, it is necessary that the wavelength of light emitted by the light source falls within the range of 350 nm through 500 nm (conditional formula (3)), and xcfx862/xcex falls within the range of 0.5 mm through 3 mm (conditional formula (4)), and, also, it is preferable that RMS(wavefront aberration) falls equal to or smaller than 0.2 (conditional formula (5)). That is, in order to reduce the spot diameter, the numerical aperture NA should be larger and, thereby, the diameter of beam incident on the scanning imaging optical system should be larger. However, if so, imaging of the beam spot is easily affected by the wavefront aberration. Accordingly, it is necessary to reduce the wavefront aberration.
As an example, change in spot diameter in the main scan direction due to the defocus when a semiconductor laser emitting light having a wavelength xcex=500 (nm) is used as the light source, calculated with RMS(wavefront aberration) as a parameter, will now be shown as a list:
FIG. 3 shows these results.
In this example, xcex=500 (nm), the target spot diameter xcfx86=20 (xcexcm), xcfx862/xcex=0.8. When RMS(wavefront aberration)xe2x89xa60.2, it is possible to expect the defocus range (allowable depth) equal to or larger than approximately 0.9 mm even when the allowable range of variation in spot diameter is assumed as xcfx86(1xc2x10.125); the allowable maximum spot diameter: 22.5 xcexcm. When the RMS(wavefront aberration) exceeds 0.2, as well as increase in variation in spot diameter, degradation in allowable depth such as the depth curve expressing relationship between spot diameter and defocus becoming remarkably asymmetrical with respect to positive/negative of defocus, occur.
The above-mentioned conditional formula (6) will now be discussed.
The above-described formula (2A) holds when xcex8=0 and cos xcex8=1. With regard to the sub-scan direction, it is possible to set so that the scanning beam is perpendicular to the surface to be scanned (xcex8=0) through all the scanning range. However, with regard to the main scan direction, there are many cases where xcex8xe2x89xa00 for the reason that the optical components should be reduced in size, and so forth. In such cases, the depth in the main scan direction is a product of the conditional formula (2) and power of cos xcex8, and the allowable depth is reduced. Accordingly, it is preferable that the conditional formula (6) is satisfied as a result of the scanning angle, power distribution and sizes of optical components and so forth being determined appropriately.
Other objects and further features of the present invention will become more apparent from the following detailed description when read in conjunction with the accompanying drawings.